document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190800>Question 1190800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Differentiate the following with the respect of x.<BR>\n" );
document.write( "a) (2-√x)^6<BR>\n" );
document.write( "b) 1/(1-1/x)^3<BR>\n" );
document.write( "c)1/2(3x-2)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822508 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Differentiate\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-sqrt%28x%29%29%5E6 ALIGN=MIDDLE  ALT=\"%282-sqrt%28x%29%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%28%282+-+sqrt%28x%29%29%5E6%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%28%282+-+sqrt%28x%29%29%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ..........apply the chain rule\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282+-sqrt%28x%29%29%5E5%28d%2Fdx%29%282-sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"6%282+-sqrt%28x%29%29%5E5%28d%2Fdx%29%282-sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%282+-+sqrt%28x%29%29=-1%2F%282sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%282+-+sqrt%28x%29%29=-1%2F%282sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282+-+sqrt%28x%29%29%5E5%2A%28-1%2F%282sqrt%28x%29%29%29 ALIGN=MIDDLE  ALT=\"6%282+-+sqrt%28x%29%29%5E5%2A%28-1%2F%282sqrt%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%282+-+sqrt%28x%29%29%5E4%2A%281%2Fsqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"-3%282+-+sqrt%28x%29%29%5E4%2A%281%2Fsqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%283+%282+-+sqrt%28x%29%29%5E5%29%2Fsqrt%28x%29 ALIGN=MIDDLE  ALT=\"+-%283+%282+-+sqrt%28x%29%29%5E5%29%2Fsqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281-1%2Fx%29%5E3 ALIGN=MIDDLE  ALT=\"1%2F%281-1%2Fx%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28d%2Fdx%29+%281%2F%281-1%2Fx%29%5E3%29 ALIGN=MIDDLE  ALT=\"+%28d%2Fdx%29+%281%2F%281-1%2Fx%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........... apply exponent rule: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa=a%5E-1 ALIGN=MIDDLE  ALT=\"1%2Fa=a%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29+%28%281-1%2Fx%29%5E-3%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29+%28%281-1%2Fx%29%5E-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .........apply the chain rule\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%28%281-1%2Fx%29%5E4%29%28d%2Fdx%29%281-1%2Fx%29 ALIGN=MIDDLE  ALT=\"-3%2F%28%281-1%2Fx%29%5E4%29%28d%2Fdx%29%281-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%281-1%2Fx%29=1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%281-1%2Fx%29=1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%28%28%28x-1%29%2Fx%29%5E4%29%281%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"-3%2F%28%28%28x-1%29%2Fx%29%5E4%29%281%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......simplify\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%28%28x-1%29%5E4%2Fx%5E4%29%281%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"-3%2F%28%28x-1%29%5E4%2Fx%5E4%29%281%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%28%28x-1%29%5E4%2Fx%5E4%29%281%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"-3%2F%28%28x-1%29%5E4%2Fx%5E4%29%281%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E4%2F%28%28x-1%29%5E4%29%281%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"-3x%5E4%2F%28%28x-1%29%5E4%29%281%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....simplify\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2F%28%28x-1%29%5E4%29 ALIGN=MIDDLE  ALT=\"-3x%5E2%2F%28%28x-1%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "assuming you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%283x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"1%2F%282%283x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28d%2Fdx%29%281%2F%282%283x-2%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"+%28d%2Fdx%29%281%2F%282%283x-2%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........take the constant out <BR>\n" );
document.write( " <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28d%2Fdx%29%281%2F%283x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28d%2Fdx%29%281%2F%283x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....... apply exponent rule\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28d%2Fdx%29%28%283x-2%29%5E-2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28d%2Fdx%29%28%283x-2%29%5E-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........apply the chain rule\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28-2%2F%28%283x-2%29%5E3%29%29%28d%2Fdx%29%283x-2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-2%2F%28%283x-2%29%5E3%29%29%28d%2Fdx%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%283x-2%29=3 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%283x-2%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%28-2%283x-2%29%5E3%29%29%283%29 ALIGN=MIDDLE  ALT=\"%282%2F%28-2%283x-2%29%5E3%29%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......simplify\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F%28%283x-2%29%5E3%29%29%283%29 ALIGN=MIDDLE  ALT=\"%28-1%2F%28%283x-2%29%5E3%29%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%283x-2%29%5E3 ALIGN=MIDDLE  ALT=\"-3%2F%283x-2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );